I don't know about anybody else, but I always feel incomplete without a whole shitload of ASL stuff with me at an ASL event. That's why so far I have always driven, not flown, to ASL events.
You can fit a heck of a lot of ASL stuff in a big suitcase, though, if you want to check a bag. That includes a set of laminated unmounted mapboards, all your counters (if you use small planos, not those honking ones that so many people like), and a huge chunk of scenarios, as well as dice tower, rulebook, etc.
Things to do to decrease size, weight, etc.:
1. Have a travel set of counters. This is a complete set of counters, except in small quantities--i.e., you don't need to bring all your 4-6-7 squads. At your option, you can leave out those incredibly rare vehicles altogether.
2. Laminated unmounted mapboards.
3. Scenario books. I scanned in all my scenarios (2100 or so), then printed them out, two sided, in color. I then bound them into books, using a comb binder. This is lightweight and compact. Of course, you needn't bring all your scenarios. If you have them all scanned in, you can easily print out a subset at any time and bind them. I just printed out 61 scenarios I wanted to play for ASLOK, and made a book. Voila. Of course, you can always eschew printing, and just bring your laptop with all those scenarios in it.
4. Bound rulebook. Much less bulky and more portable than all those huge monstrosities of binders with page protectors, etc.
